On Quantum-MV Algebras - Part I: The Orthomodular Algebras

Abstract

We prove that almost all the properties of quantum-MV algebras are verified by orthomodular algebras, the new algebras introduced in a previous paper. We put a special insight on transitive antisymmetric orthomodular (taOM) algebras, generalizations of MV algebras. We make the connection with IMTL and NM algebras. In memoriam Dragos. Vaida (1933 – 2020)

Keywords

• m-mel algebra
• m-be algebra
• m-abe algebra
• m-prebck algebra
• m-bck algebra
• m-bck lattice
• imtl algebra
• nm algebra
• mv algebra
• (w nm)mv algebra
• quantum-mv algebra
• orthomodular algebra
• taom algebra
• boolean algebra